Download Scientific Notation 1. Which of the following best represents the

Scientific Notation
1. Which of the following best represents the speed of a banana slug?
A. 2 × 10-5 kilometers per second
B. 2 × 105 meters per second
C. 2 × 10-5 meters per second
D. 2 × 105 kilometers per second
2. The equatorial radius of Mars is 3,394 km. Which of the following would be a reasonable
estimate for the equatorial radius of Mars?
A. 3 × 10-3 km
B. 3 × 10-4 km
C. 3 × 104 km
D. 3 × 103 km
3. The display on a calculator screen is shown below.
3.37508EE9
What number does the calculator display represent?
A. 3,375,080,000
B. 0.0000000034
C. 337,508,000,000,000
D. 0.0000000003
4. Visible blue light has a wavelength of about 0.0000475 centimeters.
What is this measurement written in scientific notation?
A. 4.75 × 104 centimeters
B. 4.75 × 10-5 centimeters
C. 4.75 × 10-4 centimeters
D. 4.75 × 105 centimeters
5. The display on a calculator screen is shown below.
3.751872EE-6
What number does the calculator display represent?
A. 0.0000037519
B. 375,187.2
C. 0.0000003752
D. 3,751,872
6. Which shows the expression below simplified?
0.0043 + (2.6 × 10-4)
A. 4.56 × 10-4
B. 4.56 × 10-3
C. 2.6043 × 10-4
D. 2.6043 × 10-7
8. The Earth is approximately 2 × 107 km from Venus at its closest approach. The Earth is also
about 4 × 1013 km from Proxima Centauri, a star. Which of the following is true?
A. The distance from Earth to Proxima Centauri is approximately two trillion times the
distance from Earth to Venus.
B. The distance from Earth to Proxima Centauri is approximately two billion times the
distance from Earth to Venus.
C. The distance from Earth to Proxima Centauri is approximately two thousand times
the distance from Earth to Venus.
D. The distance from Earth to Proxima Centauri is approximately two million times the
distance from Earth to Venus.
9. The length of an object is measured as 24.7 centimeters. What is this measurement in
scientific notation?
A. 247 × 101 centimeters
B. 2.47 × 101 centimeters
C. 0.247 × 102 centimeters
D. 2,470 × 102 centimeters
10. Which shows the expression below in simplified form?
(6 × 106) × (4 × 10-2)
A. 2.4 × 105
B. 10 × 104
C. 2.4 × 106
D. 2.4 × 104
Answers
1. C
2. D
3. A
4. B
5. A
6. B
8. D
9. B
10. A
Explanations
1. A banana slug moves very slowly, so its speed is best represented by a very small number.
Therefore, 2 × 10-5 meters per second best represents the speed of a banana slug.
2. First, round the radius of Mars to the thousands place.
3,394 km
3,000 km
Then, write each option in standard notation.
3 × 10-4 km = 0.0003 km
3 × 10-3 km = 0.003 km
3 × 103 km = 3,000 km
3 × 104 km = 30,000 km
Therefore, 3 × 103 km is the best estimate for the equatorial radius of Mars.
3. The calculator display represents a number in scientific notation where 10 is raised to the
power given after the EE symbol.
3.37508EE9 = 3.37508 × 109
Convert the number to standard notation by moving the decimal point 9 places to the right.
3.37508 × 109 = 3,375,080,000
Therefore, the calculator display represents the number 3,375,080,000.
4. A number is written in scientific notation when it is expressed in the form shown below,
where a is greater than or equal to 1 and less than 10, and n is an integer.
a × 10n
To write 0.0000475 as a number greater than or equal to 1 and less than 10, move the decimal
point 5 places to the right, and then multiply by 10-5 to offset moving the decimal point.
0.0000475 centimeters = 4.75 × 10-5 centimeters
5. The calculator display represents a number in scientific notation where 10 is raised to the
power given after the EE symbol.
3.751872EE-6 = 3.751872 × 10-6
Convert the number to standard notation by moving the decimal point 6 places to the left.
3.751872 × 10-6 = 0.0000037519
Therefore, the calculator display represents the number 0.0000037519.
6. First, convert 0.0043 to scientific notation.
0.0043 + (2.6 × 10-4) = (4.3 × 10-3) + (2.6 × 10-4)
Next, convert (4.3 × 10-3) so the exponent is the same as the exponent in the second number.
(4.3 × 10-3) + (2.6 × 10-4) = (43 × 10-4) + (2.6 × 10-4)
Then, complete the addition.
(43 × 10-4) + (2.6 × 10-4) = 45.6 × 10-4
Finally, convert to scientific notation.
45.6 × 10-4 = 4.56 × 10-3
7.
Convert all of the values in scientific notation to standard notation.
To help visualize this, think of it in terms of meters instead of millimeters. Remember, 1 meter is
equal to 1,000 millimeters.
The only reasonable option is 5.6 meters per second, or 5.6 × 103
slow.
. The other options are too
8. Compare the distance from Earth to Proxima Centauri to the distance from Earth to Venus by
dividing the distance to Proxima Centauri by the distance to Venus.
Since 2 × 106 is equal to 2,000,000, the distance from Earth to Proxima Centauri is
approximately two million times the distance from Earth to Venus.
9. A number is written in scientific notation when it is expressed in the form shown below,
where a is greater than or equal to 1 and less than 10, and n is an integer.
a × 10n
To write 24.7 centimeters as a number greater than or equal to 1 and less than 10, move the
decimal point 1 place to the left, and then multiply by 101 to offset moving the decimal point.
24.7 centimeters = 2.47 × 101 centimeters
10. First, group the numbers multiplied by powers of 10 together, and then group the powers of
10 together.
(6 × 106) × (4 × 10-2) = (6 × 4) × (106 × 10-2)
Then, multiply the numbers in the first set of parentheses and add the exponents of 10.
(6 × 4) × (106 × 10-2) = 24 × 106 + (-2)
= 24 × 104
Finally, convert to scientific notation.
24 × 104 = 2.4 × 105
Therefore, the simplified expression is 2.4 × 105.